Area of curved surface

Hi,

I have data points belonging to a surface in 3D. I want to calculate the surface area of it. What are my options? If possible computationally inexpensive solutions are preferred. The way I have done it so far is to fit a plane into the points, project the boundary points onto the plane and calculate the area of the resulting polygon. But I want something more precise. The X and Y data are on a regular grid, the Z data not. All three are floats.

[yuefeng Yin]

Hello,

I am working on a formula to describe the curved surface of a flat material, can you give me some XYZ data, I may calculate the whole surface area?

Answer 1

[Harsha Medikonda]

I understand that you wish to calculate the surface area of a 3D graphics object. Currently such a functionality does not exist, but you can calculate the surface area of a 2-D surface in a 3-D space. Please refer to the link below for more details

http://www.mathworks.com/matlabcentral/answers/184234-how-do-i-determine-the-surface-area-of-a-2-d-surface-in-a-3-d-space

Some other useful links:

http://www.mathworks.com/matlabcentral/answers/93117-how-can-i-calculate-the-area-of-my-surface-plot-in-matlab-7-9-r2009b

http://www.mathworks.com/help/releases/R2014a/images/ref/regionprops.html

http://www.mathworks.com/matlabcentral/answers/35501-surface-area-from-a-z-matrix

http://www.mathworks.com/help/map/ref/areaint.html

Answer 2

[Roger Stafford]

In your grid system you should be able to approximate your three-dimensional surface area as the sum of the areas of a set of triangles. If the coordinates of a triangle are P1 = [x1,y1,z1], P2 = [x2,y2,z2], P3 = [x3,y3,z3], its area is:

    1/2*norm(cross(P2-P1,P3-P1));